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Unformatted text preview: ( 3,6 ) . 7. Convert the polar curve r = 4 sin θ to cartesian coordinates, and identify it as an ellipse, parabola, or hyperbola. 8. Find the Taylor series of f ( x ) = 1 ( x + 1 ) 2 at a = 0. 9. Determine whether ∞ ∑ n = 1 (1 ) n n 2 n ! is absolutely convergent, conditionally convergent, or divergent. 10. A lake with a carrying capacity of 900 ﬁsh is stocked with 100 ﬁsh. The relative growth rate k is assumed to be equal to ln ( 2 ) per year. (a) How long will it take for the population to reach 300 ﬁsh? (Your answer should be simpliﬁed as far as possible.) (b) What would the answer to (a) be if the carrying capacity were essentially inﬁnite?...
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 Fall '08
 wang
 Math, Calculus, Trigraph, Mathematical analysis, Conic section

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